Approximation algorithms and an integer program for multi-level graph spanners

Reyan Ahmed, Keaton Hamm, Mohammad Javad Latifi Jebelli, Stephen Kobourov, Faryad Darabi Sahneh, Richard Spence

Research output: Contribution to journalArticlepeer-review

Abstract

Given a weighted graph G (V, E) and t ≥ 1, a subgraph H is a t-spanner of G if the lengths of shortest paths in G are preserved in H up to a multiplicative factor of t. The subsetwise spanner problem aims to preserve distances in G for only a subset of the vertices. We generalize the minimum-cost subsetwise spanner problem to one where vertices appear on multiple levels, which we call the multi-level graph spanner (MLGS) problem, and describe two simple heuristics. Applications of this problem include road/network building and multi-level graph visualization, especially where vertices may require different grades of service. We formulate a 0-1 integer linear program (ILP) of size O (|E|| V|2) for the more general minimum pairwise spanner problem, which resolves an open question by Sigurd and Zachariasen on whether this problem admits a useful polynomial-size ILP. We extend this ILP formulation to the MLGS problem, and evaluate the heuristic and ILP performance on random graphs of up to 100 vertices and 500 edges.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Apr 1 2019

Keywords

  • Graph spanners
  • Integer programming
  • Multi-level graph representation

ASJC Scopus subject areas

  • General

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